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2 cards from this section. Quick, good the night before a test.
What does h represent in the context of finding a derivative using the central difference formula?
Think about how we calculate the difference between points.
Given f(2) = 4 and f(2.2) = 5, what is the approximate value of f'(2)?
Use the central difference formula.
What is the central difference formula used for?
Recall its definition from our discussions.
True or False: The step size (h) affects the accuracy of numerical differentiation.
Think about the implications of our previous example.
Consider a function given by the points x = [0, 1, 2, 3] and f(x) = [0, 1, 4, 9]. Use numerical differentiation to calculate the approximate value of f'(2). What do the results tell you about the behavior of the function?
Consider the average slope between the points to determine the derivative at x = 2.
Evaluate the error in your numerical differentiation for the given function values. If h = 0.5 and you find f'(2) using central difference, how would you verify the accuracy?
Remember to analyze the difference between the calculated derivative and the true derivative.
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